Expression of type Lambda

from the theory of proveit.logic.sets.enumeration

import proveit
# Automation is not needed when building an expression:
proveit.defaults.automation = False # This will speed things up.
proveit.defaults.inline_pngs = False # Makes files smaller.
%load_expr # Load the stored expression as 'stored_expr'
# import Expression classes needed to build the expression
from proveit import Conditional, Lambda, i, j, k, x
from proveit.core_expr_types import a_1_to_i, b_1_to_j, c_1_to_k
from proveit.logic import And, Equals, Forall, InSet, Set
from proveit.numbers import Natural

# build up the expression from sub-expressions
expr = Lambda([i, j, k], Conditional(Forall(instance_param_or_params = [a_1_to_i, x, b_1_to_j, c_1_to_k], instance_expr = Equals(Set(a_1_to_i, x, b_1_to_j, x, c_1_to_k), Set(a_1_to_i, b_1_to_j, x, c_1_to_k)).with_wrapping_at(2)), And(InSet(i, Natural), InSet(j, Natural), InSet(k, Natural))))

expr:

# check that the built expression is the same as the stored expression
assert expr == stored_expr
assert expr._style_id == stored_expr._style_id
print("Passed sanity check: expr matches stored_expr")

Passed sanity check: expr matches stored_expr

# Show the LaTeX representation of the expression for convenience if you need it.
print(stored_expr.latex())

\left(i, j, k\right) \mapsto \left\{\forall_{a_{1}, a_{2}, \ldots, a_{i}, x, b_{1}, b_{2}, \ldots, b_{j}, c_{1}, c_{2}, \ldots, c_{k}}~\left(\begin{array}{c} \begin{array}{l} \left\{a_{1}, a_{2}, \ldots, a_{i}, x,b_{1}, b_{2}, \ldots, b_{j}, x,c_{1}, c_{2}, \ldots, c_{k}\right\} =  \\ \left\{a_{1}, a_{2}, \ldots, a_{i},b_{1}, b_{2}, \ldots, b_{j}, x,c_{1}, c_{2}, \ldots, c_{k}\right\} \end{array} \end{array}\right) \textrm{ if } i \in \mathbb{N} ,  j \in \mathbb{N} ,  k \in \mathbb{N}\right..

stored_expr.style_options()

no style options

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	Lambda	parameters: 1 body: 2
1	ExprTuple	32, 34, 37
2	Conditional	value: 3 condition: 4
3	Operation	operator: 5 operand: 9
4	Operation	operator: 7 operands: 8
5	Literal
6	ExprTuple	9
7	Literal
8	ExprTuple	10, 11, 12
9	Lambda	parameters: 13 body: 14
10	Operation	operator: 17 operands: 15
11	Operation	operator: 17 operands: 16
12	Operation	operator: 17 operands: 18
13	ExprTuple	27, 29, 28, 30
14	Operation	operator: 19 operands: 20
15	ExprTuple	32, 21
16	ExprTuple	34, 21
17	Literal
18	ExprTuple	37, 21
19	Literal
20	ExprTuple	22, 23
21	Literal
22	Operation	operator: 25 operands: 24
23	Operation	operator: 25 operands: 26
24	ExprTuple	27, 29, 28, 29, 30
25	Literal
26	ExprTuple	27, 28, 29, 30
27	ExprRange	lambda_map: 31 start_index: 36 end_index: 32
28	ExprRange	lambda_map: 33 start_index: 36 end_index: 34
29	Variable
30	ExprRange	lambda_map: 35 start_index: 36 end_index: 37
31	Lambda	parameter: 45 body: 38
32	Variable
33	Lambda	parameter: 45 body: 39
34	Variable
35	Lambda	parameter: 45 body: 40
36	Literal
37	Variable
38	IndexedVar	variable: 41 index: 45
39	IndexedVar	variable: 42 index: 45
40	IndexedVar	variable: 43 index: 45
41	Variable
42	Variable
43	Variable
44	ExprTuple	45
45	Variable